Stellar kinematics of X-ray bright massive elliptical galaxies

We discuss a simple and fast method for estimating masses of early-type galaxies from optical data and compare the results with X-ray derived masses. The optical method relies only on the most basic observables such as the surface brightness $I(R)$ and the line-of-sight velocity dispersion $\sigma_p(R)$ profiles and provides an anisotropy-independent estimate of the galaxy circular speed $V_c$. The mass-anisotropy degeneracy is effectively overcome by evaluating $V_c$ at a characteristic radius $R_{\rm sweet}$ defined from {\it local} properties of observed profiles. The sweet radius $R_{\rm sweet}$ is expected to lie close to $R_2$, where $I(R) \propto R^{-2}$, and not far from the effective radius $R_{\rm eff}$. We apply the method to a sample of five X-ray bright elliptical galaxies observed with the 6-m telescope BTA-6 in Russia. We then compare the optical $V_c$-estimate with the X-ray derived value, and discuss possible constraints on the non-thermal pressure in the hot gas and configuration of stellar orbits. We find that the average ratio of the optical $V_c$-estimate to the X-ray one is equal to $\approx 0.98$ with $11 \%$ scatter, i.e. there is no evidence for the large non-thermal pressure contribution in the gas at $\sim R_{\rm sweet}$. From analysis of the Lick indices H$\beta$, Mgb, Fe5270 and Fe5335, we calculate the mass of the stellar component within the sweet radius. We conclude that a typical dark matter fraction inside $R_{\rm sweet}$ in the sample galaxies is $\sim 60\%$ for the Salpeter IMF and $\sim 75 \%$ for the Kroupa IMF.